Question

factorise:- 4x2-y2+6y-9​

Answer 1

SOLUTION

TO FACTORISE

$\sf{4 {x}^{2} - {y}^{2} + 6y - 9 }$

FORMULA TO BE IMPLEMENTED

We are aware of the identities that

$\sf{1. \: {(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2} }$

$\sf{2. \: \: {a}^{2} - {b}^{2} = (a + b)(a - b) }$

EVALUATION

$\sf{4 {x}^{2} - {y}^{2} + 6y - 9 }$

$\sf{ = 4 {x}^{2} - ( {y}^{2} - 6y + 9 )}$

$\sf{ = 4 {x}^{2} - ( {y}^{2} - 2.y.3 + {3}^{2} )}$

$\sf{ = 4 {x}^{2} - {(y - 3)}^{2} } \: \: ( \: by \: identity \: 1)$

$\sf{ = {(2x)}^{2} - {(y - 3)}^{2} } \: \:$

$\sf{ = (2x + y - 3)(2x - y + 3)} \: \: (by \: identity \: 2)$

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